Deformed algebra and the effective dynamics of the interior of black holes

Abstract

We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar–Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling two-spheres, provided that the deformation parameters are chosen to be negative.